MinT - Best Known (35, 35+42, s)-Nets in Base 32

Best Known (35, 35+42, s)-Nets in Base 32

(35, 35+42, 196)-Net over F₃₂ — Constructive and digital

Digital (35, 77, 196)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 28, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (7, 49, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(35, 35+42, 288)-Net in Base 32 — Constructive

(35, 77, 288)-net in base 32, using

14 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
- base change [i] based on digital (9, 65, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(35, 35+42, 352)-Net over F₃₂ — Digital

Digital (35, 77, 352)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(35, 35+42, 92462)-Net in Base 32 — Upper bound on s

There is no (35, 77, 92463)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 78 819256 436944 341927 960911 163079 868420 810322 312713 460069 383519 467336 405837 931176 159641 884014 255183 942238 405959 331436 > 32⁷⁷ [i]